Motivated by Proximal Alternating Predictor-Corrector (PAPC) [1]}, [2]}, the min-max optimization problem (REF ) can be solved by the following fixed-point equations
\(\left\lbrace \begin{array}{l}\mathbf {F}=\mathbf {F}-\nabla h_s(\mathbf {F})-\frac{\partial \langle \mathbf {p}, \mathbf {u}\rangle }{\partial \mathbf {F}}, \\\mathbf {u} = \text{prox}_{h^{*}_{f}}\big (\mathbf {u}+ \mathbf {\Delta _{s}} SF(\mathbf {F})\big ).\end{array}\right.\) 
